Prep the pan and oven: Heat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment, leaving overhang for easy lifting.
Lightly grease.
Melt butter and chocolate: In a heatproof bowl set over a pot of simmering water, melt the butter and chopped chocolate, stirring until smooth. Remove from heat and let cool 5 minutes.
Whisk in sugars: Stir the granulated and brown sugar into the warm chocolate mixture until glossy and combined.
Add eggs and vanilla: Whisk in the eggs one at a time, then the vanilla. Mix just until incorporated; don’t overbeat.
Fold in dry ingredients: Sift the flour, cocoa, salt, and espresso powder over the bowl.
Gently fold with a spatula until no dry streaks remain.
Bake the brownies: Spread batter evenly in the pan. Bake 24–30 minutes, until the edges are set and a toothpick comes out with a few moist crumbs. Do not overbake.
Cool completely in the pan on a rack.
Toast the pecans: While brownies cool, toast pecans on a baking sheet at 350°F for 7–9 minutes, until fragrant. Cool, then chop.
Make the topping custard: In a medium saucepan, whisk evaporated milk, egg yolks, and sugar. Add butter.
Cook over medium heat, whisking constantly, until thickened and bubbling gently, 8–12 minutes. The mixture should coat the back of a spoon.
Finish the topping: Remove from heat. Stir in vanilla, salt, coconut, and pecans.
Let cool 10–15 minutes to thicken slightly.
Assemble: Spread the topping over the cooled brownies. Chill 1–2 hours to set for cleaner slices.
Slice and serve: Use the parchment to lift brownies out. Cut with a sharp knife, wiping the blade between cuts.